Real Positive Semidefinite Matrix Cone
Why
The set of positive semidefinite matrices turns out to be a cone in the vector space of $n \times n$ matrices.
Main result
$\mathbfsf{S} _+^d$ is a convex, pointed, closed
cone with interior $\mathbfsf{S} _{++}^d$ relative
to $\mathbfsf{S} ^d$.1
The cone of positive definite matrices is open.
- Future editions will contain a proof. ↩︎